package com.hit.basmath.learn.recursion_i;

/**
 * 70. Climbing Stairs
 * <p>
 * You are climbing a stair case. It takes n steps to reach to the top.
 * <p>
 * Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
 * <p>
 * Note: Given n will be a positive integer.
 * <p>
 * Example 1:
 * <p>
 * Input: 2
 * Output: 2
 * <p>
 * Explanation: There are two ways to climb to the top.
 * 1. 1 step + 1 step
 * 2. 2 steps
 * <p>
 * Example 2:
 * <p>
 * Input: 3
 * Output: 3
 * <p>
 * Explanation: There are three ways to climb to the top.
 * 1. 1 step + 1 step + 1 step
 * 2. 1 step + 2 steps
 * 3. 2 steps + 1 step
 */
public class _70 {
    public int climbStairs(int n) {
        // base cases
        if (n <= 0) return 0;
        if (n == 1) return 1;
        if (n == 2) return 2;

        int one_step_before = 2;
        int two_steps_before = 1;
        int all_ways = 0;

        for (int i = 2; i < n; i++) {
            all_ways = one_step_before + two_steps_before;
            two_steps_before = one_step_before;
            one_step_before = all_ways;
        }
        return all_ways;
    }
}
